Johanna Michor and Gerald Teschl On the Equivalence of Different Lax Pairs for the Kac-van Moerbeke Hierarchy (24K, LaTeX2e) ABSTRACT. We give a simple algebraic proof that the two different Lax pairs for the Kac-van Moerbeke hierarchy, constructed from Jacobi respectively super-symmetric Dirac-type difference operators, give rise to the same hierarchy of evolution equations. As a byproduct we obtain some new recursions for computing these equations.